> What does it mean to factor vectors exactly?

I was thinking about a*unit_vector + b*unit_vector -> (a+b)*unit_vector

But as you said there are many others that do not make sense for vectors.

> In contrast the other way has proven to work in physics.quantum.  They're
> both reasonable.

And also in diffgeom.

In any case, both of this methodologies seem ok to me (create new
Add/Mul or reuse Add/Mul), but both of them are not what is proposed
in general terms on the wiki describing the API (a ScalarField and
Vector what eagerly eat anything that operates on them, i.e.
ScalarField+ScalarField -> ScalarField).

>
>
> On Tue, Jun 11, 2013 at 9:21 AM, Stefan Krastanov
> <krastanov.ste...@gmail.com> wrote:
>>
>> This is also one of the ways to go forward. I personally dislike it
>> because:
>>
>> - A non trivial amount of functionality needs reimplementation
>> (flatten for instance)
>> - We do not have "standard correct way" to interface with functions
>> like factor, symplify, had, get, atoms, etc, so it is hard to be sure
>> that you have implemented everything
>> - As a personal preference, I actually like "garbage in - garbage out"
>>
>> But this way has been proven to work in matrix expressions and is also
>> used in Pernici's tensor module, so I am not against it.
>>
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